punctele M apatinand axei OX vor avea coordonatele (x;0)
atunci lungimile patratelor segmentelor AM si BM vor fi
AM²= (x-2)²+ (0-3)²= (x-2)²+9
BM²=(x-4)²+ (0-5)²=(x-4)²+25
introducand aceste valori in relatia data, avem
(x-2)²+9+(x-4)²+25=54
adica
(x-2)²+(x-4)²=54-25-9=54-34=20
x²-4x+4+x²-8x+16=20
2x²-12x=20-20
2x²-12x=0 |:2
x²-6x=0
x(x-6)=0
x1=0
x2=6
deci punctele sunt M1(0.0)≡O (0;0) si , respectiv , M2(6;0)
prin "≡" am inteles "identic"
verificare
pt M1
2²+3²+4²+5²=54
4+9+16+25=54
4+25+25=54
54=54 adevarat
pt M2 (6.0)
4²+3²+2²+5²=54 adevarat (deja verificat , datorita comutativitatii adunarii)
adevarate ambele, problema este bine rezolvata
